Question: Simplify the following expression: $q = \dfrac{z^2 + 2z - 35}{z + 7} $
Answer: First factor the polynomial in the numerator. $ z^2 + 2z - 35 = (z + 7)(z - 5) $ So we can rewrite the expression as: $q = \dfrac{(z + 7)(z - 5)}{z + 7} $ We can divide the numerator and denominator by $(z + 7)$ on condition that $z \neq -7$ Therefore $q = z - 5; z \neq -7$